In many magnetic resonance imaging (MRI) applications, a given region of the body is imaged repeatedly to capture its time variations. For example, such dynamic applications include functional MRI (in which brain changes are induced by a time-varying paradigm), time-resolved angiography (in which changes in the blood vessels are caused by the passage of a bolus of contrast agent), and cardiac imaging (in which the heart changes as it beats, and also possibly as a bolus of contrast agent passes through it). The temporal resolution of the MRI, i.e. the time to acquire a time frame, should be good enough to capture the important features of the temporal changes. In the event that the readily available temporal resolution proves insufficient, there exist many dynamic MRI methods able to improve it. Some of these methods include UNFOLD, parallel imaging (e.g. SMASH, SENSE, SPACE-RIP) and partial-Fourier imaging techniques. Through some assumption(s) and/or the use of prior information, these methods allow a fraction of the required data to be calculated instead of measured. This reduction in the amount of acquired data usually translates directly into a corresponding reduction in the time to acquire the data and thus can improve the temporal resolution, and/or the total scan time.
Possibly due to its simplicity and fast processing speed, Cartesian SENSE may be the most commonly used parallel imaging method. Cartesian SENSE is typically limited to Cartesian, regular sampling schemes. More general methods such as SPACERIP or general SENSE can be used to reconstruct data acquired along more complicated trajectories in k-space. Recently, non-Cartesian sampling schemes such as variable-density SMASH, GRAPPA and others have allowed sensitivity information to be obtained as part of the dynamic acquisition by sampling more densely the center of k-space than the outer regions. These “self-calibrated” methods do not require the acquisition of a reference scan to measure the coil sensitivity; instead, coil sensitivity is preferably calculated directly from the fully sampled region around the center of k-space, in the dynamically acquired data set.
A regular Cartesian sampling scheme 10 is shown in FIG. 1A in which only one k-space line 12 out of every four is sampled. FIG. 1B shows the resulting image 20 from one of the coils. The image 20 is corrupted by aliasing artifacts resulting from sampling only 24 k-space lines rather than 96. As described in the publication SENSE: sensitivity encoding for fast MRI, 42 MAGN RESON MED 952 (1999) by Klaas P. Pruessmann et al., Cartesian SENSE can be used to separate the four overlapped spatial locations at each image pixel to reconstruct a full, de-aliased image. FIG. 1C shows an image 30 that was reconstructed and de-aliased using Cartesian SENSE.
FIG. 2A shows another sampling technique 40 that is similar to the technique 10 used in FIG. 1A with the exception that all of the missing k-space locations 42 are filled with zeros before applying a Fourier transform (FT). As a consequence of the presence of the zeros, a full field of view (FOV) is reconstructed in the image 50 shown in FIG. 2B instead of the smaller, acquired FOV of the image 20 in FIG. 1B.
In an alternative method, the four overlapped spatial locations at each pixel of the image 50 in FIG. 2B could be separated by keeping only the non-aliased pixel and discarding the remaining three aliased pixels. This method and the method described above for FIG. 1B are mathematically equivalent, and lead to numerically identical treated images 30 and 60 as shown in FIGS. 1C and 2C.
Typically, it is desirable to use a Cartesian sampling function because of the simplicity of calculations associated with the data reconstruction. Other known non-cartesian sampling methods, such as SPACERIP and the general version of SENSE allow data acquired with a non-Cartesian sampling scheme to be reconstructed into images, but require a significantly larger number of calculations to do so. While variable-density SMASH and GRAPPA do allow the use of a sampling strategy that departs from a Cartesian grid, these methods make the approximation that coil sensitivities can be combined to emulate functions that are related to Fourier basis functions, an approximation absent in the SENSE/SPACERIP approach.